Square Root Calculator › Square root of 6
Square Root of 6
√6 ≈ 2.44949
6 is not a perfect square, so √6 is an irrational number that is approximately 2.44949. In simplified radical form, √6 = √6.
√6 lies between √4 = 2 and √9 = 3.
| Number | 6 |
| Square root (decimal) | 2.44949 |
| Simplified radical | √6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 6
6 = 2 × 3. This is what determines the simplified radical: for √6 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √6 is already in simplest radical form as √6.
Estimating √6 by hand
√6 falls between √4 = 2 and √9 = 3, so it starts at 2.something. The Babylonian method refines that guess by averaging it with 6 ÷ the guess:
| Step | Estimate |
| Start | 2 |
| Step 1 | 2.5 |
| Step 2 | 2.45 |
| Step 3 | 2.44949 |
After 3 steps the estimate is 2.44949, matching √6 ≈ 2.44949.
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Frequently asked questions
Is 6 a perfect square?
No, 6 is not a perfect square, so its square root is irrational and approximately 2.44949.
What is the square root of 6 in simplest radical form?
√6 = √6 in simplest radical form.